Question

The scores on a psychology exam were normally distributed with a mean of 62 and a standard deviation of 9. A failing grade on the exam was anything 2 or more standard deviations below the mean. What was the cutoff for a failing score? Approximately what percentage of the students failed? The cutoff for a failing score was 44. (Simplify your answer.) Approximately percent of the students failed. (Round to one decimal place as needed.)

Answer 1

Solution :

Given that ,

b) P(x < 44 )

= P[(x - $\mu$ ) / $\sigma$ < (44 - 62) / 9 ]

= P(z < -2.0)

Using z table,

= 0.0228

percentage = 2.28%

Approximately 2.3% of the students failed